Class 7 Maths · Original EZT practice
Working with Fractions (Class 7 Chapter 8): summary and practice
How far does someone walk in five and a half hours at three km an hour? Chapter 8 teaches multiplying and dividing fractions and using them in everyday problems. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 7). Older Class 7 books numbered chapters differently - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Multiplication of fractions
Multiply the numerators and multiply the denominators, then simplify. The word of means multiply: half of three-quarters is a half times three-quarters.
2. Division of fractions
Dividing by a fraction means multiplying by its reciprocal - flip the second fraction. Division asks how many times one amount fits inside another.
3. Problems involving fractions
Read the story, decide whether to multiply or divide, then check that the size of the answer makes sense.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Multiply two fractions
Choose the method: Multiply the tops, multiply the bottoms, then simplify.
EZT practice question
Find two-thirds times three-fifths.
Show the worked solution
- Tops: two times three is six.
- Bottoms: three times five is fifteen.
- Six fifteenths simplifies to two-fifths.
Answer: Two-fifths.
Check: Six fifteenths and two-fifths are the same fraction.
Watch for this: Do not add the numerators; multiplication is not addition.
Now try it yourself
Find three-quarters times eight-ninths.
Check your answer
Two-thirds.
Twenty-four thirty-sixths simplifies to two-thirds.
Read of as multiply
Choose the method: Replace the word of with a multiplication sign.
EZT practice question
Half of three-quarters of a pizza is eaten. How much of the whole pizza is that?
Show the worked solution
- Of means multiply: a half times three-quarters.
- Tops one times three is three; bottoms two times four is eight.
Answer: Three-eighths of the pizza.
Check: Half of three-quarters must be smaller than three-quarters, and three-eighths is.
Watch for this: Do not take half of the whole pizza; the half applies to the three-quarters.
Now try it yourself
Find a third of five-sixths.
Check your answer
Five eighteenths.
One times five is five; three times six is eighteen.
Multiply a mixed number by a whole number
Choose the method: Convert the mixed number to an improper fraction first.
EZT practice question
Find two and a half times four.
Show the worked solution
- Two and a half is five-halves.
- Five-halves times four is twenty-halves.
- Twenty-halves is ten.
Answer: Ten.
Check: Two and a half groups of four: two fours are eight, plus half of four is two, giving ten.
Watch for this: Do not multiply only the whole part and forget the fraction.
Now try it yourself
Find three and a third times six.
Check your answer
Twenty.
Three and a third is ten-thirds; ten-thirds times six is twenty.
Divide by a fraction using the reciprocal
Choose the method: Flip the divisor and multiply.
EZT practice question
Find three-quarters divided by a half.
Show the worked solution
- The reciprocal of a half is two.
- Three-quarters times two is six-quarters.
- Six-quarters is one and a half.
Answer: One and a half.
Check: One and a half halves make three-quarters.
Watch for this: Do not flip the first fraction; only the divisor flips.
Now try it yourself
Find two-thirds divided by one-sixth.
Check your answer
Four.
Two-thirds times six is four.
Ask how many times one amount fits in another
Choose the method: Divide the total by the size of one part.
EZT practice question
How many quarter-litre glasses fill three litres?
Show the worked solution
- Divide three by a quarter.
- Three times four is twelve.
Answer: Twelve glasses.
Check: Four quarter-litres make one litre, so three litres need twelve.
Watch for this: Do not multiply three by a quarter; fitting asks for division.
Now try it yourself
How many half-kg packets can be filled from seven kg?
Check your answer
Fourteen.
Seven divided by a half is seven times two.
Divide a fraction by a whole number
Choose the method: The whole number is a fraction with denominator one; flip it.
EZT practice question
Find five-sixths divided by five.
Show the worked solution
- Five is five over one; its reciprocal is one-fifth.
- Five-sixths times one-fifth is five thirtieths.
- Five thirtieths simplifies to one-sixth.
Answer: One-sixth.
Check: Sharing five-sixths equally among five gives one-sixth each.
Watch for this: Do not divide only the numerator and leave the denominator unchanged without checking.
Now try it yourself
Find three-quarters divided by six.
Check your answer
One-eighth.
Three-quarters times one-sixth is three twenty-fourths, which is one-eighth.
Solve a length problem with a mixed number
Choose the method: Convert to an improper fraction, then multiply by the used fraction.
EZT practice question
A ribbon is five and a half metres long. Two-thirds of it is used. What length is used?
Show the worked solution
- Five and a half is eleven-halves.
- Eleven-halves times two-thirds is twenty-two sixths.
- Twenty-two sixths is eleven-thirds, or three and two-thirds.
Answer: Three and two-thirds metres.
Check: The used part must be less than five and a half, and three and two-thirds is.
Watch for this: Do not multiply by three-halves; the used fraction is two-thirds.
Now try it yourself
Three-fifths of forty students are girls. How many girls?
Check your answer
Twenty-four.
Forty times three-fifths is twenty-four.
Solve a distance problem
Choose the method: Multiply the speed by the time, with the time as an improper fraction.
EZT practice question
Someone walks three km in one hour. How far do they walk in five and a half hours?
Show the worked solution
- Five and a half is eleven-halves.
- Three times eleven-halves is thirty-three halves.
- Thirty-three halves is sixteen and a half.
Answer: Sixteen and a half km.
Check: Five hours give fifteen km, and the extra half hour adds one and a half km.
Watch for this: Do not add five and a half to three; distance is speed times time.
Now try it yourself
Nine litres are poured into bottles of one and a half litres each. How many bottles?
Check your answer
Six.
Nine divided by three-halves is nine times two-thirds, which is six.
Try a mixed set
Choose a method or explanation before opening each answer.
1. How do you multiply fractions?
Show answer and reason
Multiply the numerators, multiply the denominators, then simplify.
Each dimension of the product scales separately.
2. How do you divide by a fraction?
Show answer and reason
Multiply by its reciprocal.
Division asks how many times the divisor fits.
3. What does of mean in a fraction problem?
Show answer and reason
Multiply.
A fraction of something is that fraction times the thing.
4. How do you handle mixed numbers?
Show answer and reason
Convert them to improper fractions first.
The rules work directly on improper fractions.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Find three-quarters times eight-ninths.
- How many half-kg packets can be filled from seven kg?
- A tank holds twelve litres and a jug holds three-quarters of a litre - how many jugs fill the tank?
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Questions about this practice page
- How do you multiply fractions?
- Multiply the numerators, multiply the denominators, then simplify.
- How do you divide by a fraction?
- Multiply by its reciprocal - flip the second fraction.
- What does of mean in a fraction problem?
- It means multiply.
- How do you handle mixed numbers?
- Convert them to improper fractions before multiplying or dividing.
- Are these the NCERT exercise questions for Working with Fractions (Class 7)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.